Finite Group Databasebeta

C2×#20241529 #26136484

order12032
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241529

Splittings

FittingC22×C32×C47 ⋊ C2
SylowC47 ⋊ C2×#1401

Subgroups

subgroupG/H
centerC2×C16D188
commutatorC4×C47C22×C16
FrattiniC2×C16C22×D47
FittingC22×C32×C47C2
socleC22×C47C22⋊C16
prime radicalC2×#10625350C8
cosocleC2×C16×C47C23
hypercenterC22×C32D47
hypocenterC47C2×#1401
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C16 ◁ C22×C16 ◁ C22×C32

294 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 89774);